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Biotechnology Letters (2006) 28: 335–340
DOI 10.1007/s10529-005-5932-2
Ó Springer 2006
Kinetic analysis of the ex vivo expansion of human hematopoietic stem/
progenitor cells
Raquel Gonc¸alves1,2, , Cla´udia Lobato da Silva1,2, , Bruno S. Ferreira1, Maria Ame´lia
N.D.A. Lemos1, Francisco Lemos1, Grac¸a Almeida-Porada1 & Joaquim M.S. Cabral1,*
1
Centro de Engenharia Biolo´gica e Quı´mica, Instituto Superior Te´cnico, Av. Rovisco Pais, 1049-001 Lisboa,
Portugal
2
Department of Animal Biotechnology, University of Nevada, Reno 89557 USA
*Author for correspondence (Fax: +351-218419062; E-mail: joaquim.cabral@ist.utl.pt)
Received 28 October 2005; Revisions requested 3 November 2005; Revisions received 5 December 2005; Accepted 6 December 2005
Key words: cell expansion, expansion kinetics model, human hematopoietic cells, human stem cells, stroma
Abstract
The total cell expansion of human umbilical cord blood (CB) and adult bone marrow (BM) CD34+enriched cells cultured in supplemented serum-free media, either over irradiated human feeder layers or in
stroma-free systems, were characterized by a simple kinetic model using only two parameters: the speciﬁc
cell expansion rate, l, and the death rate constant, kk. Both CB and BM cells can expand at approximately
the same rate (0.21 day)1) in this culture system however, cell death depends on the presence of stroma and
the environment in which the cells are cultured.
Introduction
The human body consumes an average of 400 billion mature blood cells per day and this number
dramatically increases under conditions of stress
(McAdams et al. 1996). Hematopoiesis consists in
a complex scheme of cell proliferation and diﬀerentiation to fulﬁl this demand in which, the more
primitive cells – hematopoietic stem/progenitor
cells (HSC) – mature into erythrocytes and the
other blood cells. The potential clinical applications of HSC include bone marrow (BM) transplantation and somatic cell gene therapy (Lewis
et al. 2001), whereas more mature blood cells are
required in speciﬁc clinical settings, e.g. blood
transfusion. Therefore, HSC ex vivo expansion
and/or diﬀerentiation is required in order to obtain a therapeutically signiﬁcant amount of cells
from the available donor samples.
These authors contributed equally to this work.
The human hematopoietic stem cell pool is
characterized by the expression of the CD34
surface antigen (Berenson et al. 1988); however,
since the expression of this marker by this population is not exclusive, a combination of CD34
and other antigens is currently used to select
HSC. One of the most used is CD38, a marker
for hematopoietic commitment (Shih et al. 1999);
thus, the more immature hematopoietic progenitors are known by the CD34+CD38- phenotype.
The HSC microenvironment in the BM consists in mesenchymal tissue composed of a mixed
population of endothelial cells, ﬁbroblasts, reticular cells, macrophages and adipocytes, known as
stromal cells. These cells support and regulate
self-renewal and differentiation of HSC, through
cell-to-cell interactions and expression of speciﬁc
cytokines and growth factors (Majumdar et al.
1998). Therefore, to mimic hematopoietic environment in vitro, stromal cells have been used as supportive cells of HSC cultures in a two-dimensional
reconstitution of the BM microenvironment
336
in vivo (Emerson 1996, Majumdar et al. 1998,
Lobato da Silva et al. 2005). In this study, human
stroma was used as feeder layer for expansion of
HSC collected from CB and BM (Lobato da Silva
et al. 2005).
Rational approaches to the ex vivo expansion
of HSC require a better understanding of selfrenewal/diﬀerentiation mechanisms. Detailed
kinetic models can provide a signiﬁcant insight
into the limiting steps involved in cell expansion
and diﬀerentiation (Lobato da Silva et al. 2003).
This information is useful not only for the in
vitro expansion itself, but also for the design and
operation of stem cell bioreactors (Cabrita et al.
2003).
In the present work we have characterized the
total cell expansion by means of a Monod-type
kinetic model involving only two parameters: the
speciﬁc cell expansion rate, l, and the death constant, kk. The parameters obtained were used to
evaluate the inﬂuence of the presence/absence of
a human feeder layer on the overall hematopoietic cell (HC) expansion. This kind of approach
is limited by the fact that, in the present case, the
cells expand but also diﬀerentiate and, thus, the
expansion rate is likely to change as the cells
evolve. However, an average value of the expansion rate can be obtained from this type of models, providing a global measure of culture system
performance in terms of total cell expansion
ex vivo.
Materials and methods
Cell preparation
Umbilical cord blood samples were obtained
after mother’s informed consent from the Pediatric Stem Cell Transplant Program, at Duke
University Medical Center, Durham, USA, and
from the Servic¸o de Ginecologia e Obstetrı´ cia,
Hospital D. Estefaˆnia, Lisboa, Portugal. Heparinized human bone marrow was obtained from
healthy donors after informed consent. Low
density cord blood mononuclear cells (CB
MNC) or bone marrow mononuclear cells (BM
MNC) were separated by a Ficoll density gradient (1.077 g ml)1) (Sigma) and washed twice in
Iscove’s Modiﬁed Dulbecco’s Medium (IMDM),
(Gibco Laboratories). CB MNC and BM MNC
from each donor were enriched for CD34+ cells
using magnetic cell sorting (Miltenyi Biotec
Inc.).
Cell expansion
A human stroma based cell culture system established for the ex vivo expansion of HSC was used
(Lobato da Silva et al. 2005). CB and BM
CD34+ enriched cells were resuspended in a serum-free medium (5 ml), QBSF-60 (Quality
Biological, Gaithersburgh, MD, USA), supplemented with stem cell factor (SCF, 100 ng ml)1),
leukaemia inhibitory factor (LIF, 10 U ml)1),
ﬁbromyalgia syndrome-related tyrosine kinase 3
ligand (Flt-3 ligand, 100 ng ml)1) and basic
ﬁbroblast growth factor (bFGF, 5 ng ml)1)
(Peprotech, Rocky Hill, NJ, USA), and cultured
over a c-irradiated feeder layer (15 Gy) or in
stroma-free conditions. The cultures were inoculated in T25 culture ﬂasks (25 cm2) in a humidiﬁed incubator at 37 °C, with an atmosphere of
5% CO2 during 2–4 weeks, maintaining periodic
half-feed procedure. The ex vivo expansion of the
cell populations was determined at each time
point by microscopic cell counting and viability
checked by Trypan Blue Dye exclusion. In order
to better visualize the expansion of cells, the
data were corrected to account for the half-feed
procedure and expressed as total cell expansion
(Lobato da Silva et al. 2003).
Cell phenotype was determined using monoclonal antibodies against CD34 and CD38
antigens (Becton Dickinson Immunochemistry
Systems, San Jose, CA, USA) and analysis was
performed in a ﬂow cytometer (FACScan, Beckton Dickinson).
Expansion kinetic model
A ﬁrst order Monod-type kinetic model for cell
expansion and death was used to compute the
concentration of viable (Xv) and dead (Xk) cells
over time (t). The balance for both viable and
dead cells can be written as
dXv
¼ l Xv kk Xv ¼ ðl kk ÞXv
dt
ð1Þ
dXk
¼ kk Xv
dt
ð2Þ
337
where t is the culture time. Assuming that both l
and kk are time invariant, integrating Equation
(1) between t = 0, Xv = X0 and t = t, Xv = Xv
leads to:
Xv ¼ X0 eðlkk Þt
ð3Þ
By substituting Equation (3) in Equation (2), the
following relation is obtained:
dXk
¼ kk X0 :eðlkk Þt
dt
ð4Þ
This equation can be integrated between t = 0,
Xk = 0 (100% viability upon culture inoculation) and t = t, Xk = Xk leading to:
h
i
X0
Xk ¼ kk
eðlkk Þt 1 ¼ kk K
l kk
ð5Þ
from which the value of kk can be estimated;
Equations (3) and (5) allow the estimation of
both l and kk.
Parameter estimation was carried out by nonlinear least-squares regression, using an Excel
spreadsheet. Conﬁdence intervals for the parameters thus obtained were computed using the
bootstrap resampling technique (Press et al.
1992).
Results and discussion
We have established a stroma-based culture
system that allows the ex vivo expansion of HSC,
from both CB and BM (Lobato da Silva et al.
2005). Signiﬁcant CB cell expansion was only
observed in the presence of a stromal layer; with
respect to BM cells, although cell expansion was
observed either in the presence or in the absence
of stroma, higher total expansion values were
obtained when cells were cultured over a feeder
cell layer.
Since CB cells could not be expanded under
stroma-free conditions, only the expansion
parameters for CB CD34+-enriched cells
expanded over human feeder cells were estimated
in this work (Table 1). Figure 1 illustrates the
model ﬁtting to the experimental values for a
representative experiment of CB CD34+-enriched
cells. The l values ranged from 0.14 to
0.24 day)1, whereas kk ranged from 0.004 to
0.035 day)1. These results suggest that the initial
cell number is not determining for total cell
expansion, since within the range of starting cell
concentration, 0.18–2.54 105 cells ml)1, l variations fall within the experimental error.
The same procedure was used with the results
of BM cultures with and without a stromal layer.
Table 1. Cord Blood (CB) and Bone Marrow (BM) expansion parameters estimated when culturing diﬀerent initial cell numbers in
the presence (+)/absence ()) of human stroma layers (n.d., not determined).
Starting population
CB
CB
CB
CB
CB
BM
BM
BM
BM
BM
BM
BM
BM
BM
Stroma
No.
X0 (cells)
1
2
3
4
5
1
1
2
2
3
4
5
6
7
1.2 106
9.0 104
7.5 105
1.27 106
8.5 105
3.25 106
3.25 106
1.76 106
1.76 106
6.2 106
2.5 106
9.3 105
4.3 106
1.7 106
%CD34+CD38)
n.d.
n.d.
n.d.
n.d.
0.23
23
23
8.2
8.2
7.4
1.7
0
0.65
0.63
+
+
+
+
+
)
+
)
+
+
+
+
+
+
The estimated parameters are given together with their 95% conﬁdence interval.
Expansion parameters
l (day)1)
kk (day)1)
0.21 ± 0.13
0.24 ± 0.04
0.19 ± 0.05
0.15 ± 0.03
0.14 ± 0.05
0.36 ± 0.03
0.30 ± 0.16
0.24 ± 0.03
0.21 ± 0.02
0.13 ± 0.02
0.14 ± 0.02
0.17 ± 0.03
0.11 ± 0.03
0.30 ± 0.06
0.013 ± 0.003
0.035 ± 0.011
0.031 ± 0.006
0.011 ± 0.003
0.004 ± 0.001
0.057 ± 0.005
0.020 ± 0.003
0.057 ± 0.006
0.024 ± 0.008
0.009 ± 0.003
0.005 ± 0.001
0.008 ± 0.001
0.014±0.003
0.015±0.002
338
3.0x10 7
Total
Viable
Dead
Total
Viable
Dead
2.5x107
2.0x107
X 1.5x107
1.0x107
5.0x106
0
0
10
5
15
20
25
Time (days)
Fig. 1. Example of model ﬁtting (lines) to the experimental
time course values of total ( ), viable ( ) and dead ( ) cell
numbers (X) for the CB no. 2 experiment expanded over a
stromal layer.
Figure 2 depicts an example of the model ﬁtting.
Table 1 shows that l values range from 0.11 to
0.36 day)1 and, although the two data points for
higher initial cell number (BM no.3 and BM
no.6) are among the ones that have a lower l value, there does not seem to be a systematic variation.
Within the range of starting cell concentration
that was used, the speciﬁc expansion rates of BM
CD34+-enriched cells are similar to the CBCD34+-enriched cells, and an average l value of
0.21 day)1 can be estimated for both CB and
BM CD34+-enriched cells. Two BM cultures
were performed without a stromal layer: both
from the values in Table 1 and from Figures 3
1.8 x10
8
1.6 x10
8
1.4 x10
8
1.2 x10
8
1.0 x10
8
8.0 x10
7
6.0 x10
7
4.0 x10
7
2.0 x10
7
Total
Viable
Dead
Total
X
Viable
Dead
0
0
2
4
6
8
10
12
14
Time (days)
Fig. 2. Example of model ﬁtting (lines) to the experimental
time course values of total ( ), viable ( ) and dead ( ) cell
numbers (X) for BM no. 7 experiment expanded over a stromal layer.
and 4, the l values seem to be slightly higher
than the corresponding experiments using a stromal layer, but still fall within the same range.
Since it was observed that a higher fold-increase
was observed for cultures with a stromal layer,
this suggests that expansion rate, l, might not be
the only determining factor for cell expansion
performance in terms of fold increase values.
Other parameters, such as the death rate (kk),
also aﬀect the outcome of hematopoietic cell
expansion.
The values of kk for BM experiments with a
stromal layer varied between 0.005–0.024 day)1
and, again, no signiﬁcant inﬂuence of the initial
cell number was observed. However, cell death
in the absence of a stromal layer seems to
be signiﬁcantly higher (0.057 day)1), which
explains why total expansion is lower when no
stromal layer is present. Also in the case of kk,
the values obtained for BM stroma containing
cultures seem to fall within the same range as
those for CB, and an average of 0.016 day)1
was estimated.
The speciﬁc constants for both cell growth
(l) and cell death (kk), determined by the
Monod-type kinetic model are in accordance
with the kinetic constants calculated by a predictive kinetic model developed to interpret
HSC expansion and diﬀerentiation (Lobato da
Silva et al. 2003) and correspond to the time
average of the respective rate constants for the
expansion and death of the diﬀerent types of
cells generated in culture. The conclusion that
death rates are determining in the total foldincrease is also in accordance with the observations in the predictive model.
Stromal cells can induce positive or negative
effects on hematopoiesis, but the mechanism of
these interactions are not fully established (Stein
et al. 2004, Moore et al. 2005). Yoo et al. (2003)
reported apoptosis suppressing eﬀects of stromal
cells which are, globally, in accordance with the
reduced kk values obtained in our studies for cultures over a stromal layer.
Our results do not allow the identiﬁcation of
any clear relation between initial cell number and
level of stem/progenitor enrichment and the
expansion rate, suggesting that, globally, HSC
from two different sources, BM and CB, can be
expanded at the same rate in this culture system.
However, our data quantitatively indicates the
339
0.50
0.45
0.40
0.35
µ
(day–1)
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0
1
2
3
4
5
6
7
X0 x 10 –6
Fig. 3. Total cell expansion growth rates as a function of the initial cell number (X0) for the cultures over irradiated feeder cells.
( ) CB with stromal layer, ( ) BM with no stromal layer and ( ) BM with stromal layer. Horizontal line corresponds to the average of all values. Vertical bars correspond to estimated errors in the parameters as obtained by the bootstrap technique.
0.07
0.06
0.05
kk
(day –1)
0.04
0.03
0.02
0.01
0.00
0
1
2
3
4
5
6
7
X 0 x 10–6
Fig. 4. Death rates as a function of the initial cell number (X0) for the cultures over irradiated feeder cells. ( ) CB with stromal
layer, ( ) BM with no stromal layer and ( ) BM with stromal layer. Horizontal line corresponds to the average of the values for
all experiments with a stromal layer. Vertical bars correspond to estimated errors in the parameters as obtained by the bootstrap
technique.
cell death dependency on the environment in
which the cells are cultured.
The model presented here only addresses
expansion and death of the total pool of hematopoietic cells in culture and does not address the
phenotype distribution of the culture over time,
namely the fraction of more primitive cells in the
total population. Nevertheless, this two-parameter model can be used to extract quantitative
information, through the estimation of meaning-
ful kinetic parameters, from experiments in
which the ex vivo expansion/maintenance of HSC
is studied.
Acknowledgements
This work was supported by Fundac¸a˜o para a
Cieˆncia e a Tecnologia (project POCTI/EQU/
38063/2001, and grants SFRH/BPD/6253/2001,
340
SFRH/BD/6209/2001 and SFRH/BD/6210/2001
awarded to B.S. Ferreira, R. Gonc¸alves and C.
Lobato da Silva), respectively. The authors gratefully acknowledge CB sample supply from the
Hospital D. Estefaˆnia in particular the nursery
team of Servic¸o de Ginecologia e Obstetrı´ cia.
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